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A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia (Distinguished Dissertations)

Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the Principia) contains a prose-style mixture of geometric and limit reasoning that has often been viewed as logically vague.In A Combination of Geometry Theorem Proving and Nonstandard Analysis, Jacques Fleuriot presents a formalization of Lemmas and Propositions from the Principia using a combination of methods from geometry and nonstandard analysis. The mechanization of the procedures, which respects much of Newton's original reasoning, is developed within the theorem prover Isabelle. The application of this framework to the mechanization of elementary real analysis using nonstandard techniques is also discussed.

Combinations of Intelligent Methods and Applications: Proceedings of the 4th International Workshop, CIMA 2014, Limassol, Cyprus, November 2014 (at ICTAI 2014) (Smart Innovation, Systems and Technologies #46)

This volume includes extended and revised versions of the papers presented at the 4th Workshop on “Combinations of Intelligent Methods and Applications” (CIMA 2014) which was intended to become a forum for exchanging experience and ideas among researchers and practitioners dealing with combinations of different intelligent methods in Artificial Intelligence. The aim is to create integrated or hybrid methods that benefit from each of their components. Some of the existing presented efforts combine soft computing methods (fuzzy logic, neural networks and genetic algorithms). Another stream of efforts integrates case-based reasoning or machine learning with soft-computing methods. Some of the combinations have been more widely explored, like neuro-symbolic methods, neuro-fuzzy methods and methods combining rule-based and case-based reasoning. CIMA 2014 was held in conjunction with the 26th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2014).

Combinations of Intelligent Methods and Applications: Proceedings of the 2nd International Workshop, CIMA 2010, France, October 2010 (Smart Innovation, Systems and Technologies #8)

The combination of different intelligent methods is a very active research area in Artificial Intelligence (AI). The aim is to create integrated or hybrid methods that benefit from each of their components. Some of the existing efforts combine soft computing methods either among themselves or with more traditional AI methods such as logic and rules. Another stream of efforts integrates machine learning with soft-computing or traditional AI methods. Yet another integrates agent-based approaches with logic and also non-symbolic approaches. Some of the combinations have been quite important and more extensively used, like neuro-symbolic methods, neuro-fuzzy methods and methods combining rule-based and case-based reasoning. However, there are other combinations that are still under investigation, such as those related to the Semantic Web. The 2nd Workshop on “Combinations of Intelligent Methods and Applications” (CIMA 2010) was intended to become a forum for exchanging experience and ideas among researchers and practitioners who are dealing with combining intelligent methods either based on first principles or in the context of specific applications. CIMA 2010 was held in conjunction with the 22nd IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2010). Also, a special track was organized in ICTAI 2010, under the same title. This volume includes revised versions of the papers presented in CIMA 2010 and one of the short papers presented in the corresponding ICTAI 2010 special track. It also includes a paper of the editors as invited.

Combinations of Intelligent Methods and Applications: Proceedings of the 3rd International Workshop, CIMA 2012, Montpellier, France, August 2012 (Smart Innovation, Systems and Technologies #23)

The combination of different intelligent methods is a very active research area in Artificial Intelligence (AI). The aim is to create integrated or hybrid methods that benefit from each of their components. The 3rd Workshop on “Combinations of Intelligent Methods and Applications” (CIMA 2012) was intended to become a forum for exchanging experience and ideas among researchers and practitioners who are dealing with combining intelligent methods either based on first principles or in the context of specific applications. CIMA 2012 was held in conjunction with the 22nd European Conference on Artificial Intelligence (ECAI 2012). This volume includes revised versions of the papers presented at CIMA 2012.

Combinatorial Algorithms: 33rd International Workshop, IWOCA 2022, Trier, Germany, June 7–9, 2022, Proceedings (Lecture Notes in Computer Science #13270)

This book constitutes the refereed proceedings of the 33rd International Workshop on Combinatorial Algorithms, IWOCA 2022, which took place as a hybrid event in Trier, Germany, during June 7-9, 2022.The 35 papers presented in these proceedings were carefully reviewed and selected from 86 submissions. They deal with diverse topics related to combinatorial algorithms, such as algorithms and data structures; algorithmic and combinatorical aspects of cryptography and information security; algorithmic game theory and complexity of games; approximation algorithms; complexity theory; combinatorics and graph theory; combinatorial generation, enumeration and counting; combinatorial optimization; combinatorics of words; computational biology; computational geometry; decompositions and combinatorial designs; distributed and network algorithms; experimental combinatorics; fine-grained complexity; graph algorithms and modelling with graphs; graph drawing and graph labelling; network theory and temporal graphs; quantum computing and algorithms for quantum computers; online algorithms; parameterized and exact algorithms; probabilistic andrandomized algorithms; and streaming algorithms.

Combinatorial Algorithms: 28th International Workshop, IWOCA 2017, Newcastle, NSW, Australia, July 17-21, 2017, Revised Selected Papers (Lecture Notes in Computer Science #10765)

This book constitutes the refereed post-conference proceedings of the 28th International Workshopon Combinatorial Algorithms, IWOCA 2017, held in Newcastle, NSW, Australia, in July 2017.The 30 regular papers presented in this volume together with 5 invited talks were carefully reviewed and selected from 55 submissions. They were organized in topical sessions named: approximation algorithms and hardness; computational complexity; computational geometry; graphs and combinatorics; graph colourings, labellings and power domination; heuristics; mixed integer programming; polynomial algorithms; privacy; and string algorithms.

Combinatorial Algorithms: 30th International Workshop, IWOCA 2019, Pisa, Italy, July 23–25, 2019, Proceedings (Lecture Notes in Computer Science #11638)

This book constitutes the refereed post-conference proceedings of the 30th International Workshop on Combinatorial Algorithms, IWOCA 2019, held in Pisa, Italy, in July 2019. The 36 regular papers presented in this volume were carefully reviewed and selected from 73 submissions. They cover diverse areas of combinatorical algorithms, complexity theory, graph theory and combinatorics, combinatorial optimization, cryptography and information security, algorithms on strings and graphs, graph drawing and labelling, computational algebra and geometry, computational biology, probabilistic and randomized algorithms, algorithms for big data analytics, and new paradigms of computation.

Combinatorial Algorithms: 20th International Workshop, IWOCA 2009, Hradec nad Moravicí, Czech Republic, June 28--July 2, 2009, Revised Selected Papers (Lecture Notes in Computer Science #5874)

This book constitutes the revised selected papers of the 20th International Workshop on Combinatorial Algorithms, held in June/July 2009 in the castle of Hradec nad Moravicí, Czech Republic. The 41 papers included in this volume together with 5 invited papers were carefully reviewed and selected from over 100 submissions. The topics dealt with are algorithms and data structures, applications, combinatorial enumeration, combinatorial optimization, complexity theory, computational biology, databases, decompositions and combinatorial designs, discrete and computational geometry, including graph drawing, and graph theory and combinatorics.

Combinatorial Algorithms: 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5–7, 2021, Proceedings (Lecture Notes in Computer Science #12757)

This book constitutes the proceedings of the 32nd International Workshop on Combinatorial Algorithms which was planned to take place in Ottawa, ON, Canada, in July 2021. Due to the COVID-19 pandemic the conference changed to a virtual format.The 38 full papers included in this book together with 2 invited talks were carefully reviewed and selected from 107 submissions. They focus on algorithms design for the myriad of combinatorial problems that underlie computer applications in science, engineering and business.Chapter “Minimum Eccentricity Shortest Path Problem with Respect to Structural Parameters” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Combinatorial Algorithms: 31st International Workshop, IWOCA 2020, Bordeaux, France, June 8–10, 2020, Proceedings (Lecture Notes in Computer Science #12126)

This book constitutes the proceedings of the 31st International Workshop on Combinatorial Algorithms which was planned to take place in Bordeaux, France, during June 8–10, 2020. Due to the COVID-19 pandemic the conference changed to a virtual format. The 30 full papers included in this book were carefully reviewed and selected from 62 submissions. They focus on algorithms design for the myriad of combinatorial problems that underlie computer applications in science, engineering and business.

Combinatorial Algorithms: 34th International Workshop, IWOCA 2023, Tainan, Taiwan, June 7–10, 2023, Proceedings (Lecture Notes in Computer Science #13889)

This book constitutes the refereed proceedings of the 34th International Workshop on Combinatorial Algorithms, IWOCA 2023, held in Tainan, Taiwan, during June 7–10, 2023. The 33 full papers included in this book were carefully reviewed and selected from 86 submissions. They were organized in topical sections as follows: algorithms and data structures; algorithmic and combinatorical aspects of cryptography and information security; algorithmic game theory and complexity of games; approximation algorithms; complexity theory; combinatorics and graph theory; combinatorial generation, enumeration and counting; combinatorial optimization; combinatorics of words; computational biology; computational geometry; decompositions and combinatorial designs; distributed and network algorithms; experimental combinatorics; fine-grained complexity; graph algorithms and modelling with graphs; graph drawing and graph labelling; network theoryand temporal graphs; quantum computing and algorithms for quantum computers; online algorithms; parameterized and exact algorithms; probabilistic and randomized algorithms; and streaming algorithms.

Combinatorial Algorithms: 29th International Workshop, IWOCA 2018, Singapore, July 16–19, 2018, Proceedings (Lecture Notes in Computer Science #10979)

This book constitutes the refereed post-conference proceedings of the 29th International Workshop on Combinatorial Algorithms, IWOCA 2018, held in Singapore, Singapore, in July 2018. The 31 regular papers presented in this volume were carefully reviewed and selected from 69 submissions. They cover diverse areas of combinatorical algorithms, complexity theory, graph theory and combinatorics, combinatorial optimization, cryptography and information security, algorithms on strings and graphs, graph drawing and labelling, computational algebra and geometry, computational biology, probabilistic and randomised algorithms, algorithms for big data analytics, and new paradigms of computation.

Combinatorial Algorithms: 22th International Workshop, IWOCA 2011, Victoria, Canada, July 20-22, 2011, Revised Selected Papers (Lecture Notes in Computer Science #7056)

This book constitutes the thoroughly referred post-workshop proceedings of the 22nd International Workshop on Combinatorial Algorithms, IWOCA 2011, held in Victoria, BC, Canada, in July 2011. The 30 revised full papers presented were carefully reviewed and selected from a total of 71 submissions. A broad variety of topics in combinatorics and graph theory are addressed, such as combinatorics on words, string algorithms, codes, Venn diagrams, set partitions; Hamiltonian & Eulerian properties, graph drawing, colouring, dominating sets, spanning trees, and others.

Combinatorial Algorithms: 21st International Workshop, IWOCA 2010, London, UK, July 26-28, 2010, Revised Selected Papers (Lecture Notes in Computer Science #6460)

This book constitutes the thoroughly referred post-proceedings of the 21st International Workshop on Combinatorial Algorithms, IWOCA 2010, held in London, UK, in July 2010. The 31 revised full papers presented together with extended abstracts of 8 poster presentations were carefully reviewed and selected from a total of 85 submissions. A broad variety of combinatorial graph algorithms for the computations of various graph features are presented; also algorithms for network compuation, approximation, computational geometry, games, and search are presented and complexity aspects of such algorithms are discussed.

Combinatorial Algorithms: 25th International Workshop, IWOCA 2014, Duluth, MN, USA, October 15-17, 2014, Revised Selected Papers (Lecture Notes in Computer Science #8986)

This book constitutes the thoroughly refereed post-workshop proceedings of the 25th International Workshop on Combinatorial Algorithms, IWOCA 2014, held in Duluth, MN, USA, in October 2014. The 32 revised full papers presented were carefully reviewed and selected from a total of 69 submissions. The papers focus on topics such as Algorithms and Data Structures, Combinatorial Enumeration, Combinatorial Optimization, Complexity Theory (Structural and Computational), Computational Biology, Databases (Security, Compression and Information Retrieval), Decompositions and Combinatorial Designs, Discrete and Computational Geometry, as well as Graph Drawing and Graph Theory. IWOCA is a yearly forum for researchers in designing algorithms field to advance creativeness of intersection between mathematics and computer science. This is the first time this conference is being held in U.S.

Combinatorial Algorithms: Generation, Enumeration, and Search (Discrete Mathematics And Its Applications Ser. #7)

This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as:CombinationsPermutationsGraphsDesignsMany classical areas are covered as well as new research topics not included in most existing texts, such as:Group algorithmsGraph isomorphismHill-climbingHeuristic search algorithmsThis work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.

Combinatorial Algorithms: Generation, Enumeration, and Search

This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as:CombinationsPermutationsGraphsDesignsMany classical areas are covered as well as new research topics not included in most existing texts, such as:Group algorithmsGraph isomorphismHill-climbingHeuristic search algorithmsThis work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.

Combinatorial Algorithms: 24th International Workshop, IWOCA 2013, Rouen, France, July 10-12, 2013. Revised Selected Papers (Lecture Notes in Computer Science #8288)

This book constitutes the thoroughly refereed post-workshop proceedings of the 24th International Workshop on Combinatorial Algorithms, IWOCA 2013, held in Rouen, France, in July 2013. The 33 revised full papers presented together with 10 short papers and 5 invited talks were carefully reviewed and selected from a total of 91 submissions. The papers are organized in topical sections on algorithms on graphs; algorithms on strings; discrete geometry and satisfiability.

Combinatorial Algorithms: 26th International Workshop, IWOCA 2015, Verona, Italy, October 5-7, 2015, Revised Selected Papers (Lecture Notes in Computer Science #9538)

This book constitutes the thoroughly refereed post-workshop proceedings for the 26 International Workshop on combinatorial Algorithms, IWOCA 2015, held in Verona, Italy, in October 2015.The 29 revised full papers presented were carefully reviewed and selected from a total of 90 submissions. The topics of the papers include algorithms and data structures (including sequential, parallel, distributed, approximation, probabilistic, randomised, and on-line algorithms), algorithms on strings and graphs; applications (bioinformatics, music analysis, networking, and others); combinatorics on words; combinatorial enumeration; combinatorial optimization; complexity theory; computational biology; compression and information retrieval; cryptography and information security; decompositions and combinatorial designs; discrete and computational geometry; graph drawing and labeling; graph theory.

Combinatorial Algorithms: 27th International Workshop, IWOCA 2016, Helsinki, Finland, August 17-19, 2016, Proceedings (Lecture Notes in Computer Science #9843)

This book constitutes the proceedings of the 27th International Workshop on Combinatorial Algorithms, IWOCA 2016, held in Helsinki, Finland, in August 2016. The 35 papers presented in this volume were carefully reviewed and selected from 87 submissions. They were organized in topical sessions named: computational complexity; computational geometry; networks; enumeration; online algorithms; algorithmic graph theory; dynamic programming; combinatorial algorithms; graph algorithms; combinatorics; and probabilistics.

Combinatorial Algorithms: 23rd International Workshop, IWOCA 2012, Krishnankoil, India, July 19-21, 2012, Revised Selected Papers (Lecture Notes in Computer Science #7643)

This book constitutes the thoroughly referred post-workshop proceedings of the 23rd International Workshop on Combinatorial Algorithms, IWOCA 2012, held in Krishnankoil, Tamil Nadu, India, in July 2012. The 32 revised full papers presented were carefully reviewed and selected from a total of 88 submissions. The papers are organized in topical sections in algorithms and data Structures, applications (including Bioinformatics, Networking, etc.), combinatorics of words and strings, combinatorial optimization, combinatorial enumeration, decompositions and combinatorial designs, complexity theory (structural and computational), computational biology and graph theory and combinatorics submissions.

Combinatorial Algorithms: 35th International Workshop, IWOCA 2024, Ischia, Italy, July 1–3, 2024, Proceedings (Lecture Notes in Computer Science #14764)

This book constitutes the refereed proceedings of the 35th International Workshop on Combinatorial Algorithms, IWOCA 2024, held in Ischia, Italy, during July 1–3, 2024. The 40 full papers included in this book were carefully reviewed and selected from 110 submissions. The IWOCA conference series has provided an annual forum for researchers who design algorithms to address the myriad combinatorial problems underlying computer applications in science, engineering, and business.

Combinatorial and Algorithmic Aspects of Networking: Third Workshop, CAAN 2006, Chester, UK, July 2, 2006, Revised Papers (Lecture Notes in Computer Science #4235)

This book constitutes the thoroughly refereed post-proceedings of the Third Workshop on Combinatorial and Algorithmic Aspects of Networking, held in Chester, UK in July 2006, co-located with the 13th Colloquium on Structural Information and Communication Complexity, SIROCCO 2006. The 10 revised full papers and one invited lecture cover a range from the Web graph to game theory to string matching, all in the context of large-scale networks.

Combinatorial and Algorithmic Aspects of Networking: First Workshop on Combinatorial and Algorithmic Aspects of Networking, CAAN 2004, Banff, Alberta, Canada, August 5-7, 2004, Revised Selected Papers (Lecture Notes in Computer Science #3405)

Combinatorial and Algorithmic Aspects of Networking: 4th Workshop, CAAN 2007, Halifax, Canada, August 14, 2007, Revised Papers (Lecture Notes in Computer Science #4852)

This book constitutes the thoroughly refereed post-conference proceedings of the 4th Workshop on Combinatorial and Algorithmic Aspects of Networking, CAAN 2007, held in Halifax, Canada, in August 2007, co-located with the 10th Workshop on Algorithms and Data Structures, WADS 2007. The main focus is on strategies for searching in networks, and for cleaning networks of unwanted intruders, on different routing strategies, and on scheduling and load balancing.